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Popular >

simplify ln(-9e^{-t})

Solution

simplify

ln (- 9 e^{- t})

Solution

2 ln (3) - t

Solution steps

ln (- 9 e^{- t})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (- 9 e^{- t}) = ln (9) + ln (e^{- t})

= ln (9) + ln (e^{- t})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{- t}) = - t ln (e)

= ln (9) - t ln (e)

t ln (e) = t

= ln (9) - t

ln (9) = 2 ln (3)

= 2 ln (3) - t

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Frequently Asked Questions (FAQ)

What is ln(-9e^{-t}) ?
The solution to ln(-9e^{-t}) is 2ln(3)-t